Suppose the cumulative distribution function of a random variable X is given by F(x) = 0 if x <0 = 0.5x if 0 =1 (a)

1. Suppose the cumulative distribution function of a random variable X is given by

F(x) = 0 if x<0

= 0.5x if 0<=x<1

= 1 if x>=1

(a) Is X a discrete random variable? Is X a continuous random variable? Why?

(b) Compute P (X 0.5).

(c) Compute P (X > 1/3).

(d) Compute P (X = 0.5).

(e) Compute P (X = 1).

(f) Compute P(0 X 0.75).

(g) ComputeP(0.5X<1).